A chemist makes 460 mL of magnesium fluoride (MgF2) working solution by adding distilled water to 20.0 mL of a 18.8 umol/L stock solution of magnesium chloride in water. Calculate the concentration of the chemist’s working solution. Round your answer to the 3 significant digits
First, let's convert the volume of the stock solution from mL to L:
20.0 mL = 20.0 mL * (1 L / 1000 mL) = 0.0200 L
Next, let's convert the concentration of the stock solution from umol/L to mol/L:
18.8 umol/L = 18.8 * 10^-6 mol/L = 1.88 * 10^-5 mol/L
Now we can calculate the amount of magnesium chloride in the stock solution:
amount of magnesium chloride = concentration * volume = 1.88 * 10^-5 mol/L * 0.0200 L = 3.76 * 10^-7 mol
Since magnesium fluoride has a 1:2 molar ratio with magnesium chloride, the amount of magnesium fluoride in the working solution is twice the amount of magnesium chloride:
amount of magnesium fluoride = 2 * 3.76 * 10^-7 mol = 7.52 * 10^-7 mol
Finally, we can calculate the concentration of the working solution by dividing the amount of magnesium fluoride by the volume of the working solution:
concentration = amount of magnesium fluoride / volume of working solution
= 7.52 * 10^-7 mol / 0.460 L
= 1.63 * 10^-6 mol/L
Rounded to three significant digits, the concentration of the chemist's working solution is 1.63 * 10^-6 mol/L.